Uniqueness of Specific Interfacial Area–Capillary Pressure–Saturation Relationship Under Non-Equilibrium Conditions in Two-Phase Porous Media Flow

Vahid Joekar-Niasar, S. Majid Hassanizadeh

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55 Scopus citations


The capillary pressure-saturation (P c-S w) relationship is one of the central constitutive relationships used in two-phase flow simulations. There are two major concerns regarding this relation. These concerns are partially studied in a hypothetical porous medium using a dynamic pore-network model called DYPOSIT, which has been employed and extended for this study: (a) P c-S w relationship is measured empirically under equilibrium conditions. It is then used in Darcy-based simulations for all dynamic conditions. This is only valid if there is a guarantee that this relationship is unique for a given flow process (drainage or imbibition) independent of dynamic conditions; (b) It is also known that P c-S w relationship is flow process dependent. Depending on drainage and imbibition, different curves can be achieved, which are referred to as "hysteresis". A thermodynamically derived theory (Hassanizadeh and Gray, Water Resour Res 29: 3389-3904, 1993a) suggests that, by introducing a new state variable, called the specific interfacial area (a nw, defined as the ratio of fluid-fluid interfacial area to the total volume of the domain), it is possible to define a unique relation between capillary pressure, saturation, and interfacial area. This study investigates these two aspects of capillary pressure-saturation relationship using a dynamic pore-network model. The simulation results imply that P c-S w relation not only depends on flow process (drainage and imbibition) but also on dynamic conditions for a given flow process. Moreover, this study attempts to obtain the first preliminary insights into the global functionality of capillary pressure-saturation-interfacial area relationship under equilibrium and non-equilibrium conditions and the uniqueness of P c-S w-a nw relationship. © 2012 The Author(s).
Original languageEnglish (US)
Pages (from-to)465-486
Number of pages22
JournalTransport in Porous Media
Issue number2
StatePublished - Feb 23 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-017-12
Acknowledgements: The authors are members of the International Research Training Group NUPUS, financed by the German Research Foundation (DFG) and The Netherlands Organization for Scientific Research (NWO). This research was also partly funded by a King Abdullah University of Science and Technology (KAUST) Center-in-Development Award to Utrecht University (Grant No. KUK-C1-017-12).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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